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The plane of the equator is defined by the earth's equator. The plane of the ecliptic is defined by the orbit of the earth and the sun. For all practical purposes the plane of the equator and the plane of the ecliptic maintain a constant inclination relative to each other of approximately 23.5°. The plane of the horizon is centred on the native, and is tangential to the earth at that point. In a sphere whose radius is indefinitely large this plane may be treated as nearly equivalent to the parallel plane with its centre at the earth's center. This greatly simplifies understanding the geometry of the horoscope. Some writers on astrology have considered the effects of parallax, but most would agree that they are relatively minor; they are clearly beyond the scope of this article. The axis of the plane of the horizon has end points above, the zenith, and below, the nadir.

Using an ephemeris and a table of houses an astrologer calculates relative positions of the sun, the moon, and the planets for specific time and place in order to erect a horoscope. This diagram, called a chart is a stylized map of the heavens. The sun or the earth is placed in the centre (depending on whether the ephemeris was heliocentric or geocentric) with the remaining elements around the outside: the planets, the lunar nodes, the ascendant and midheaven, and the houses. Then the angles between the planets are designated. These angles are the astrological aspects. Different systems of tri-secting arcs produce houses of different size. The calculation of a horoscope is a complex but purely technical skill normally carried out by computer software such as Astrolabe, Kepler, WinStar or ZET. There are websites which offer automated online astrology services too, such as Astro.com.

The celestial sphere is a sphere of arbitrary radius upon which the items appearing on the horoscope are projected without regard to their distance from the native.